Island in Atlantic, originally a British-run territory (8)
I believe the answer is:
rhodesia
'a british-run territory' is the definition.
I can't judge whether this definition defines the answer.
'island in atlantic originally' is the wordplay.
'island' becomes 'rhodes' (Greek island).
'originally' indicates taking the first letters.
The first letters of 'in atlantic' is 'ia'.
'rhodes'+'ia'='RHODESIA'
Can you help me to learn more?
(Other definitions for rhodesia that I've seen before include "Former African country" , "former republic" , "former state" , "What became Zimbabwe" , "Former British colonial territory in Africa, now Zambia and Zimbabwe" .)